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A159969
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Numerator of Hermite(n, 13/24).
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1
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1, 13, -119, -9035, -14639, 10218013, 153914329, -15655840187, -513817209695, 29391432064813, 1713902824372009, -62366587629825323, -6240409786798253711, 134413599620299018045, 25111471036836549128569, -215506510190170502086043, -111283139511606108762536639
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 12^n * Hermite(n, 13/24).
E.g.f.: exp(13*x - 144*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/12)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 13/12, -119/144, -9035/1728, -14639/20736, ...
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MATHEMATICA
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Numerator[Table[HermiteH[n, 13/24], {n, 0, 30}]] (* or *) Table[12^n* HermiteH[n, 1/12], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(13*x - 144*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(13/12)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018
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CROSSREFS
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KEYWORD
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sign,frac
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AUTHOR
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STATUS
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approved
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